Question
Your originals stay on your drive. The heavy work (transcribing, reframing, exporting) runs on your PC or your phone.
Only lightweight versions for viewing and editing in the browser go to the server, along with the project data (the transcript and your sequences). With plans that include the cloud, you can also upload, download and back up your media.
If you delete a project, its exports and the lightweight versions stored on the server are deleted too. You can ask for your account to be deleted at any time.
More details in the Trust Center: Security and data.